Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen
Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen
Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen
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H&B – p.24/27Deduction cycloidSnell’s law between successive layerssinα jv j= sinα j+1v j+1, j = 1, 2,... ,NAs N → ∞ this gives another conservation law ∗sinαv= C (2)From conservation laws (1) en (2) will obtainparametrized curveα ↦→ (x(α),h(α))∗ Think of translation symmetry in x–direction <strong>and</strong> Noether’s theorem